Yep, you can eat a cactus leaf. Certain kinds, anyway. The leaf pictured above is a nopal, or prickly pear. Living in California means that these delicious leaves are everywhere. Just be careful of the tiny (#$!!%!!@#$!) spines when handling them and be sure and remove the dark spots where they hide with a paring knife or vegetable peeler and rinse them well before cooking. Also, whether you get the leaf in the wild or from a market, be sure to grab a leaf that is firm.
Once the leaf is cleaned you can steam the whole thing or cook it for a few minutes in some butter, oil or even bacon fat. Recently I cooked this one up with some olive oil, onion, and a bit of chicken broth and then strained out the liquid to serve the cactus and onions over beef tacos. I removed the outer skin for that meal but next time I'm going to steam one with the skin on and try that out.
One thing to keep in mind: The cooked meat of the cactus is slimy like okra. It may not be your thing. There are other cooking methods that eliminate the slime such as frying, washing, or giving them a light char on the grill. As an okra fan, I found the tart leaf a great addition to my tacos. Also, that slime is part of the nutritional content of the leaves which are full of vitamins. I'm looking forward to using another leaf in a meal soon.